AS
Andrey L. Shilnikov
nlin.CDModels, Neurologicalmath.DSq-bio.NCNonlinear Dynamicsnlin.AOModels, BiologicalPeriodicitynlin.PSblended approach
On Valency
published · living versionsW_u8w65yxq·v1 · currentpublished
Delay-induced multirhythmicity in a 3-cell inhibitory network
with Xinxin Qie, Morten Gram Pedersen, Jian Song, Shenquan Liu
1 version
Preprints & journals
52 papers in the corpus · 2004–2026Hierarchical emergence of network bursting in a four-cell central pattern generator model2609.13858v1 · Krishna Pusuluri, Huiwen Wu, Andrey L. Shilnikov2026 · 0 citationsarXiv
On a stable torus in a 3D system with a saddle-focus.42455018 · Shilnikov, Andrey L, Shilnikov, Leonid P2026 · 0 citationsChaos (Woodbury, N.Y.). 2026;36(7)
Synaptic delays shape dynamics and function in multimodal neural motifs.40168609 · Qie, Xinxin, Zang, Jie, Liu, Shenquan et al.2025 · 6 citationsChaos (Woodbury, N.Y.). 2025;35(4)
Widespread neuronal chaos induced by slow oscillating currents.40053010 · Scully, James, Hinsley, Carter, Bloom, David et al.2025 · 5 citationsChaos (Woodbury, N.Y.). 2025;35(3)
Correction: Bourahmah et al. Error Function Optimization to Compare Neural Activity and Train Blended Rhythmic Networks. Brain Sci. 2024, 14, 468.39595925 · Bourahmah, Jassem, Sakurai, Akira, Katz, Paul S et al.2024 · 0 citationsBrain sciences. 2024;14(11)
Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits. A tutorial.38983123 · Scully, James, Bourahmah, Jassem, Bloom, David et al.2024 · 4 citationsFrontiers in network physiology. 2024;4:1397151
Error Function Optimization to Compare Neural Activity and Train Blended Rhythmic Networks.38790447 · Bourahmah, Jassem, Sakurai, Akira, Katz, Paul S et al.2026 · 1 citationBrain sciences. 2024;14(5)
Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus2307.14518v1 · Carter Hinsley, James Scully, Andrey L. Shilnikov2023 · 3 citationsarXiv
Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits2211.00245v1 · James Scully, Jassem Bourahmah, David Bloom et al.2022 · 1 citationarXiv
Noise-activated barrier crossing in multiattractor dissipative neural networks.35854623 · Taylor, Joseph D, Chauhan, Ashok S, Taylor, John T et al.2022 · 4 citationsPhysical review. E. 2022;105(6-1):064203
Leonid Shilnikov and mathematical theory of dynamical chaos.35105128 · Gonchenko, Sergey, Kazakov, Alexey, Turaev, Dmitry et al.2022 · 16 citationsChaos (Woodbury, N.Y.). 2022;32(1):010402
Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing.34598438 · Scully, James J, Neiman, Alexander B, Shilnikov, Andrey L2021 · 10 citationsChaos (Woodbury, N.Y.). 2021;31(9):093121
Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems2104.11314v1 · Tingli Xing, Krishna Pusuluri, Andrey L. Shilnikov2021 · 14 citationsarXiv
Homoclinic chaos in the Rössler model.33261365 · Malykh, Semyon, Bakhanova, Yuliya, Kazakov, Alexey et al.2021 · 41 citationsChaos (Woodbury, N.Y.). 2020;30(11):113126
Generalized half-center oscillators with short-term synaptic plasticity.33075913 · Baruzzi, V, Lodi, M, Storace, M et al.2021 · 13 citationsPhysical review. E. 2020;102(3-1):032406
2-burster for rhythm-generating circuits2008.03377v1 · Aaron Kelley, Andrey L. Shilnikov2020 · 0 citationsarXiv
Poincare return maps in neural dynamics: three examples2007.05595v1 · Marina L. Kolomiets, Andrey L. Shilnikov2020 · 2 citationsarXiv
Homoclinic puzzles and chaos in a nonlinear laser model2006.13812v1 · K. Pusuluri, H.G.E. Meijer, A.L. Shilnikov2020 · 20 citationsarXiv
Design Principles for Central Pattern Generators With Preset Rhythms.31722491 · Lodi, Matteo, Shilnikov, Andrey L, Storace, Marco2021 · 44 citationsIEEE transactions on neural networks and learning systems. 2020;31(9):3658-3669
Bottom-up approach to torus bifurcation in neuron models.30384623 · Ju, Huiwen, Neiman, Alexander B, Shilnikov, Andrey L2019 · 40 citationsChaos (Woodbury, N.Y.). 2018;28(10):106317
Unraveling the Chaos-land and its organization in the Rabinovich System1806.01306v1 · Krishna Pusuluri, Arkady Pikovsky, Andrey Shilnikov2018 · 7 citationsarXiv
Homoclinic chaos and its organization in a nonlinear optics model1806.01309v1 · Krishna Pusuluri, Andrey L Shilnikov2018 · 17 citationsPhys. Rev. E 98, 040202 (2018)
Bursting dynamics in the normal and failing hearts.28725037 · Bondarenko, Vladimir E, Shilnikov, Andrey L2019 · 4 citationsScientific reports. 2017;7(1):5927
The Art of Grid Fields: Geometry of Neuronal Time.27013981 · Shilnikov, Andrey L, Maurer, Andrew Porter2016 · 24 citationsFrontiers in neural circuits. 2016;10:12
Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits1509.04514v1 · Justus T.C. Schwabedal, Drake E. Knapper, A.L. Shilnikov2015 · 22 citationsarXiv
Electrogenic properties of the Na⁺/K⁺ ATPase control transitions between normal and pathological brain states.25589588 · Krishnan, Giri P, Filatov, Gregory, Shilnikov, Andrey et al.2016 · 65 citationsJournal of neurophysiology. 2015;113(9):3356-74
Mixed mode synchronization and network bursting of neurons with post-inhibitory rebound1412.2058v1 · Roman Nagornov, Grigory Osipov, Maxim Komarov et al.2014 · 1 citationarXiv
Robust design of polyrhythmic neural circuits.25215766 · Schwabedal, Justus T C, Neiman, Alexander B, Shilnikov, Andrey L2015 · 26 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2014;90(2):022715
Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons.24985442 · Barrio, Roberto, Martínez, M Angeles, Serrano, Sergio et al.2015 · 64 citationsChaos (Woodbury, N.Y.). 2014;24(2):023128
Key bifurcations of bursting polyrhythms in 3-cell central pattern generators.24739943 · Wojcik, Jeremy, Schwabedal, Justus, Clewley, Robert et al.2015 · 75 citationsPloS one. 2014;9(4):e92918
Toward robust phase-locking in Melibe swim central pattern generator models.24387584 · Jalil, Sajiya, Allen, Dane, Youker, Joseph et al.2014 · 28 citationsChaos (Woodbury, N.Y.). 2013;23(4):046105
Voltage interval mappings for an elliptic bursting model1310.5232v1 · Jeremy Wojcik, Andrey Shilnikov2013 · 12 citationsarXiv
Showcase of Blue Sky Catastrophes1310.5233v1 · Leonid Shilnikov, Andrey Shilnikov, Dmitry Turaev2013 · 25 citationsarXiv
Symbolic Toolkit for Chaos Explorations1310.4898v1 · Tingli Xing, Jeremy Wojcik, Roberto Barrio et al.2013 · 5 citationsarXiv
Computational quest for Kaos-land1310.1122v2 · Tingli Xing, Jeremy Wojcik, Michael A. Zaks et al.2013 · 0 citationsarXiv
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial1204.3278v1 · Roberto Barrio, Andrey Shilnikov, Leonid Shilnikov2012 · 88 citationsarXiv
Spikes matter for phase-locked bursting in inhibitory neurons.22587168 · Jalil, Sajiya, Belykh, Igor, Shilnikov, Andrey2012 · 49 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2012;85(3 Pt 2):036214
Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells.22282726 · Neiman, Alexander B, Dierkes, Kai, Lindner, Benjamin et al.2014 · 42 citationsJournal of mathematical neuroscience. 2011;1(11)
Bistability of bursting and silence regimes in a model of a leech heart interneuron.22181178 · Malashchenko, Tatiana, Shilnikov, Andrey, Cymbalyuk, Gennady2012 · 33 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2011;84(4 Pt 1):041910
Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci.22060441 · Barrio, Roberto, Blesa, Fernando, Serrano, Sergio et al.2012 · 97 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2011;84(3 Pt 2):035201
Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model.22656867 · Barrio, Roberto, Shilnikov, Andrey2012 · 93 citationsJournal of mathematical neuroscience. 2011;1(1):6
Order parameter for bursting polyrhythms in multifunctional central pattern generators.21728632 · Wojcik, Jeremy, Clewley, Robert, Shilnikov, Andrey2011 · 46 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2011;83(5 Pt 2):056209
Six types of multistability in a neuronal model based on slow calcium current.21814554 · Malashchenko, Tatiana, Shilnikov, Andrey, Cymbalyuk, Gennady2011 · 59 citationsPloS one. 2011;6(7):e21782
Fast reciprocal inhibition can synchronize bursting neurons.20481777 · Jalil, Sajiya, Belykh, Igor, Shilnikov, Andrey2010 · 53 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2010;81(4 Pt 2):045201
Variability of bursting patterns in a neuron model in the presence of noise.19543963 · Channell, Paul, Fuwape, Ibiyinka, Neiman, Alexander B et al.2010 · 46 citationsJournal of computational neuroscience. 2009;27(3):527-42
Polyrhythmic synchronization in bursting networking motifs.19045494 · Shilnikov, Andrey, Gordon, René, Belykh, Igor2009 · 79 citationsChaos (Woodbury, N.Y.). 2008;18(3):037120
When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons.18764581 · Belykh, Igor, Shilnikov, Andrey2008 · 101 citationsPhysical review letters. 2008;101(7):078102
Origin of bursting through homoclinic spike adding in a neuron model.17501202 · Channell, Paul, Cymbalyuk, Gennady, Shilnikov, Andrey2007 · 104 citationsPhysical review letters. 2007;98(13):134101
Coexistence of tonic spiking oscillations in a leech neuron model.15830162 · Cymbalyuk, Gennady, Shilnikov, Andrey2005 · 88 citationsJournal of computational neuroscience. 2005;18(3):255-63
Mechanism of bistability: tonic spiking and bursting in a neuron model.16089641 · Shilnikov, Andrey, Calabrese, Ronald L, Cymbalyuk, Gennady2006 · 156 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2005;71(5 Pt 2):056214
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